Tetrahedron Mesh
Vertices - 4
Faces - 4

Cube Mesh
Vertices - 8
Faces - 12

Since, the cow in the image is rotated by 90 degrees. R_relative rotates the camera by 90 deg in the z-axis.
We also see that, the cow is centered in the image. Therefore, we keep T_relative as all 0 since there is no translation involved.

R_rel = pytorch3d.transforms.euler_angles_to_matrix(
			torch.tensor([0, 0, 0]), "XYZ"
			).numpy()

T_rel = [0, 0, 0]
Copy

The cow appears smaller, so the camera must be translated away from the cow. Therefore we some non-zero value in z-axis of T_relative i.e [0, 0, d]
Since the orientation of the cow is the same as that in the default image. The R_relative matrix will be all 0s.

R_rel = pytorch3d.transforms.euler_angles_to_matrix(
			torch.tensor([0, 0, 0]), "XYZ"
			).numpy()
T_rel = [0, 0, 2]
Copy

The cow can be seen shifted a little in the down-left direction. Hence, we translate the camera by some positive value in the x-axis and negative value in the y-axis. So, T_relative becomes [d, -d, 0]
Since the orientation of the cow is the same as that in the default image. The R_relative matrix will be all 0s.

R_rel = pytorch3d.transforms.euler_angles_to_matrix(
			torch.tensor([0, 0, 0]), "XYZ"
			).numpy()
T_rel = [0.5, -0.5, 0]
Copy

Here, we see the cow from it's right and not the front, which means we are both translating and rotating the camera.
We first need to rotate the camera by 90 deg counter-clockwise around the y-axis.
After this the cow will be to the right of the camera, so we move the camera in negative x-axis by 3 to bring it to center and in negative z-direction to bring the cow (side-view) in center of frame again.

```python
R_rel = pytorch3d.transforms.euler_angles_to_matrix(
			torch.tensor([0, -np.pi/2, 0]), "XYZ"
			).numpy()
T_rel = [3, 0, 3]
Copy

Point cloud corresponding to 1st Image -

Point cloud corresponding to 2nd Image -

Point cloud formed by union -

Torus

Equations Reference - https://www.nosco.ch/mathematics/en/torus.php

"Figure 8" immersion of the Klein Bottle

Equations Reference - https://en.wikipedia.org/wiki/Klein_bottle

Torus

Equations Reference - https://www.nosco.ch/mathematics/en/torus.php

Segment of a spring

Equations Reference - https://en.wikipedia.org/wiki/Spring_(mathematics)